44 ^f}•. Jamvs Nice on 



be modified and extended in the constant endeavour to obtain 

 a principle wide enough to bridge the gaps which constantly come 

 into view with our increasing knowledge. 



The part which continuity has played in the development of 

 Mathematics and Physics is not so well known, but students of 

 those subjects can bear testimony to the fact that without it 

 their present position would not have been attained The 

 calculus is the very embodiment of mathematical continuity, and 

 it is in the realm of the so-called " continuous functions " that it 

 has given the most striking examples of its power. The belief 

 that all physical and chemical phenomena are but continuous 

 transformations of energy from one form to another, which could 

 ultimately be explained by the laws of Dynamics, has had a pro- 

 found effect on the minds of all physicists and chemists. But 

 the struggle between discontinuity and continuity is making 

 itself felt here in a manner too marked to ignore. The desire to 

 found his subject on a vigorous and unassailable basis has of late 

 driven the mathematician from those elegant applications and 

 developments of mathematical analysis with which all inathe- 

 matical students are so familiar, to the close and careful 

 scrutiny of his methods and assumptions and the thorough study 

 of those discontinuities and singularities in mathematical functions 

 which his predecessors used to pass by with airy indifference. In 

 Physics we are faced with difficulties of a like nature. By reason 

 of the refinements of modern experimental methods older theories 

 of radiation and the heat content of bodies have been found 

 wanting. Where we previously pictured an output of energy in 

 a continuous and orderly fashion, we have now apparently to 

 postulate something of a catastrophic nature, a discontinuous 

 emission of energy, whose essentially disturbing feature is not so 

 much its suddenness, as our inability to tit it into the scheme of 

 laws and equations which have hitherto served to summarise our 

 knowledge in this branch of science. The solution of this diffi- 

 culty will, it is expected, provide us with the key to several other 

 difficulties still preventing an advance in this subject. 



